Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x - 5$ and $ KL = 7x + 3$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x - 5} = {7x + 3}$ Solve for $x$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({8}) - 5$ $ KL = 7({8}) + 3$ $ JK = 64 - 5$ $ KL = 56 + 3$ $ JK = 59$ $ KL = 59$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {59} + {59}$ $ JL = 118$